A calibration method and system for position error and amplitude-phase error of an ultra-short baseline array

Abstract

The present application discloses a method and system for calibrating position error and amplitude-phase error of an ultra-short baseline array, which relates to the field of underwater acoustic positioning technology. The method includes sequentially numbering M array elements of the ultra-short baseline array, establishing a base array coordinate system with the first array element as the reference array element, and determining the coordinate positions of each array element; fixing the ultra-short baseline array at one end of a lifting and rotating rod, fixing an auxiliary sound source at the other end, controlling the rotation angle of the ultra-short baseline array and collecting multiple groups of data; and respectively estimating the array element position error and the amplitude-phase error between each channel by using the phase difference and covariance matrix between the signals received by each array element. The present application can improve the estimation accuracy of the ultra-short baseline array.

Description

Technical Field

[0001] The present application relates to the technical field of underwater acoustic positioning, and in particular to a method and system for calibrating position error and amplitude and phase error of an ultra-short baseline array. Background Art

[0002] The research on acoustic array calibration algorithm first appeared in the application field of microphone array. Microphones belong to the category of Wireless Acoustic Sensor Networks (WASNs), which are low-cost and difficult to detect. Compared with the working environment of microphones, the underwater measurement environment is more complex, so directly transplanting the calibration algorithm of microphone arrays to sonar arrays cannot meet the requirements of high-precision calibration.

[0003] When the ultra-short baseline array is used to estimate the target azimuth in the application domain, there is a certain deviation between the actual position of each receiving hydrophone and the theoretical position. This deviation is called array error. The causes of array error include the machining errors caused by the array manufacturing process and the fact that the geometric center of each hydrophone in the array does not completely coincide with the acoustic radiation center. Due to the small size of the ultra-short baseline array, even a millimeter-level array error will bring non-negligible relative errors, which greatly reduces the accuracy of target azimuth estimation. Therefore, the impact of array error on target azimuth estimation cannot be ignored. Before using the array to locate the target, it is essential to correct the array error.

[0004] The machining errors of the array can be corrected by precision machining or high-precision optical measurement, but this can only determine the relative position of the geometric center of the primitive, and it also brings additional costs. Compared with optical measurement, the acoustic measurement method can directly obtain the relative position of the acoustic center of each hydrophone in the array, and there is no need to purchase additional precision measurement equipment to correct the array. Therefore, the acoustic measurement method is the best choice to correct array errors and improve the working performance of the acoustic array. Summary of the invention

[0005] The purpose of the present application is to provide a method and system for calibrating position error and amplitude and phase error of an ultra-short baseline array, which can improve the accuracy of ultra-short baseline array estimation.

[0006] To achieve the above objectives, this application provides the following solutions:

[0007] In a first aspect, the present application provides a method for calibrating position error and amplitude and phase error of an ultra-short baseline array, comprising the following steps:

[0008] The M array elements of the ultra-short baseline array are numbered in sequence, a base array coordinate system is established with the first array element as the reference array element, and the coordinate position of each array element is determined.

[0009] Fix the ultra-short baseline array at one end of the lifting and rotating rod, and fix the auxiliary sound source at the other end. Control the rotation angle of the ultra-short baseline array and collect multiple groups of data.

[0010] Utilize the phase differences and covariance matrix between the signals received by each element to estimate the element position error and the amplitude-phase error between each channel respectively.

[0011] Optionally, establish a base array coordinate system with the first element as the reference element, specifically including:

[0012] Take the first element as the origin of the coordinate system, set its amplitude gain as the reference value, and the initial phase as the reference phase, and establish a base array coordinate system. The position coordinates of each element in the base array coordinate system are .

[0013] Optionally, fix the ultra-short baseline array at one end of the lifting and rotating rod, and fix the auxiliary sound source at the other end. Control the rotation angle of the ultra-short baseline array and collect multiple groups of data, specifically including:

[0014] Place the ultra-short baseline array and the auxiliary sound source at the same depth in the anechoic tank.

[0015] Rotate the ultra-short baseline array through the lifting and rotating rod so that the ultra-short baseline array receives the combined signals emitted by the auxiliary sound source at each rotation angle.

[0016] Optionally, the combined signal emitted by the auxiliary sound source consists of a chirp signal and a calibration single-frequency signal with a fixed frequency.

[0017] Optionally, utilize the phase differences and covariance matrix between the signals received by each element to estimate the element position error and the amplitude-phase error between each channel respectively, specifically including:

[0018] Intercept the single-frequency signal and calculate the phase difference between each element and the reference element .

[0019] Utilize the relationship between the time delay difference of the signal arriving at each element and the phase difference, and use the least squares method to calculate the position of the element and the initial phase of each element .

[0020] Calculate the amplitude gain of each element according to the covariance matrix of the signals received by the ultra-short baseline array .

[0021] Optionally, the relationship between the time delay difference of each element and the phase difference is specifically:

[0022] .

[0023] Wherein, To calibrate the frequency of a single-frequency signal, is the time delay difference between an array element and a reference array element, is the initial phase, is the phase difference, The value of is The value of .

[0024] Optionally, the calculation formula for the time delay difference is:

[0025] .

[0026] Wherein, is the speed of sound, is the angle of rotation of the lifting and rotating rod, is the pitch angle.

[0027] Optionally, the least squares method is used to calculate the positions of the array elements and the initial phases of each array element, specifically including:

[0028] According to the formula , calculate the positions of the array elements and the initial phases of each array element.

[0029] Wherein, the matrix , the matrix , the matrix .

[0030] Optionally, according to the covariance matrix of the signals received by the ultra-short baseline array, calculate the amplitude gain of each array element, specifically including:

[0031] According to the formula , calculate the amplitude gain of each array element.

[0032] Where are the elements on the diagonal of the covariance matrix.

[0033] In a second aspect, the present application provides an ultra-short baseline array position error and amplitude-phase error calibration system, including:

[0034] A base array coordinate system construction module, configured to sequentially number M array elements of the ultra-short baseline array, establish a base array coordinate system with the first array element as the reference array element, and determine the coordinate positions of each array element.

[0035] A data acquisition module, configured to fix the ultra-short baseline array at one end of a lifting and rotating rod, fix an auxiliary sound source at the other end, control the rotation angle of the ultra-short baseline array, and acquire multiple groups of data.

[0036] An error estimation module, which is used to estimate the array element position error and the amplitude-phase error between channels respectively by using the phase difference and covariance matrix between the received signals of each array element.

[0037] According to the specific embodiments provided by the present application, the following technical effects are disclosed in the present application:

[0038] The present application provides a method and system for calibrating the position error and amplitude-phase error of an ultra-short baseline array. First, a base array coordinate system is established with the first array element as the reference array element, and the positions of each array element are determined based on this coordinate system. Accurate array element position information is the basis for subsequent error estimation and calibration, which helps to improve the positioning accuracy of the entire system. Secondly, by using the auxiliary sound source and the lifting and rotating rod, the rotation angle of the array can be conveniently controlled and multiple groups of data can be collected. These data contain the phase difference and covariance matrix information between the received signals of each array element, which are the key to estimating the array element position error and the amplitude-phase error between channels. By collecting and analyzing these data, the error situation of the system can be evaluated more accurately. Finally, the present application combines the phase difference information and the covariance matrix to estimate the array element position error and the amplitude-phase error between channels respectively. This method improves the accuracy and reliability of error estimation. Description of the Drawings

[0039] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0040] Figure 1 It is a schematic flow chart of a method for calibrating the position error and amplitude-phase error of an ultra-short baseline array provided by an embodiment of the present application.

[0041] Figure 2 It is a flow chart of an ultra-short baseline array position and amplitude-phase error calibration algorithm provided by an embodiment of the present application.

[0042] Figure 3 It is a time-domain diagram of the signal used for array calibration provided by an embodiment of the present application.

[0043] Figure 4 It is a layout diagram of the array position calibration pool experiment provided by an embodiment of the present application.

[0044] Figure 5 It is a comparison diagram of the array calibration position and the ideal position provided by an embodiment of the present application.

[0045] Figure 6Schematic diagram of functional modules of a calibration system for position error and amplitude-phase error of an ultra-short baseline array provided by an embodiment of the present application. Detailed implementation manners

[0046] Next, the technical solutions in the embodiments of the present application will be clearly and completely described with reference to the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts shall fall within the protection scope of the present application.

[0047] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below with reference to the drawings and specific implementation manners.

[0048] Embodiment 1

[0049] As Figure 1 shown, this embodiment provides an ultra-short baseline array position error and amplitude-phase error calibration method, including the following steps:

[0050] Step 101: Number the M array elements of the ultra-short baseline array in sequence, establish a base array coordinate system with the first array element as the reference array element, and determine the coordinate positions of each array element.

[0051] Step 102: Fix the ultra-short baseline array at one end of the lifting and rotating rod, fix the auxiliary sound source at the other end, control the rotation angle of the ultra-short baseline array, and collect multiple groups of data.

[0052] Step 103: Use the phase difference and covariance matrix between the signals received by each array element to estimate the array element position error and the amplitude-phase error between each channel respectively.

[0053] In the present application, as Figure 2 shown in the flowchart of the ultra-short baseline array position error and amplitude-phase error calibration method, the calibration method includes establishing a base array coordinate system, experimental data collection, data processing, and calibration result analysis. Among them, the base array coordinate system is as shown in step 101, the experimental data collection is as shown in step 102. Specifically, the experimental data collection includes equipment placement, array rotation, signal generation, and signal reception. The data processing includes signal synchronization, single-frequency signal interception, calculation of the initial phase of each array element position, and calculation of amplitude gain. The calibration result analysis includes experimental data comparison.

[0054] Among them, when performing step 101, specifically, it can be as follows:

[0055] Taking the first array element as the origin of the coordinate system, setting its amplitude gain as the reference value and the initial phase as the reference phase, establish a base array coordinate system, and the position coordinates of each array element in the base array coordinate system are 。

[0056] Specifically, the M array elements of the array are numbered in sequence, with the first array element as the reference array element, and a base array coordinate system is established to represent the coordinate positions of each array element. , and the reference array element amplitude gain and initial phase reference are set, that is , and in this embodiment, a six-element circular array with a radius is selected for error calibration example. Specifically, as Figure 5 shown in the calibration result diagram of the uniform six-element array element positions, the ideal positions of the array elements are marked with small black circles, and the actual array element positions after calibration are marked with small red circles. Among them, the first array element is used as the reference array element and is located at the coordinate origin. Therefore, the ideal position and the actual position completely coincide, that is, the red small circle and the black small circle overlap (only the red small circle is shown in the figure). In addition, in order to visually compare the ideal and actual array element positions, a large black circle is used to enclose the two in the figure.

[0057] Among them, when performing step 102, it can be specifically as follows:

[0058] First, the ultra-short baseline array and the auxiliary sound source are placed at the same depth in the anechoic water tank.

[0059] Then, the ultra-short baseline array is rotated by the lifting and rotating rod so that the ultra-short baseline array receives the combined signals emitted by the auxiliary sound source at each rotation angle. Among them, the combined signals emitted by the auxiliary sound source are composed of a chirp signal and a calibration single-frequency signal with a fixed frequency.

[0060] Specifically, placing the ultra-short baseline array and the auxiliary sound source at the same depth in the anechoic water tank can be as follows:

[0061] As Figure 4 shown in the layout diagram of the calibration experimental equipment in this embodiment, which includes an ultra-short baseline array, an auxiliary sound source, a lifting and rotating rod, and a console. The ultra-short baseline array is fixed on the lifting and rotating rod, and the auxiliary sound source is fixed at the other end, and the two are horizontally 6 meters apart. The array and the auxiliary sound source are both placed in the water at a depth of 2 meters. When the first array element is aligned with the auxiliary sound source, the angle of the console of the lifting and rotating rod is set to zero. By operating the console, the array rotates by an angle , the auxiliary sound source emits signals, and the array repeats to receive multiple groups of data.

[0062] The operator first fixes the array on the lifting and rotating rod and puts it into the water at the same depth as the auxiliary sound source at a far-field distance, ensuring that the signals emitted by the auxiliary sound source reach the array in an approximate plane wave propagation mode. When the first array element is aligned with the auxiliary sound source by controlling the rotating rod, the angle of the console of the lifting and rotating rod is set to zero.

[0063] The signal emitted by the auxiliary sound source consists of a chirp signal and a frequency Composed of calibrated single-frequency signals. In this embodiment, the frequency range of the chirp signal is 13 kHz to 16 kHz. The frequency of the calibrated single-frequency signal must be such that the half-wavelength of the signal is greater than the element spacing. In this embodiment, the element spacing is 40 mm, and kHz is selected as the calibrated single-frequency signal.

[0064] Control the rotation angle of the lifting and rotating rod , at each rotation angle, the auxiliary sound source emits a signal, and the array repeatedly receives multiple groups of data. The rotation angle of the array is equivalent to the auxiliary sound source being placed at position.

[0065] Among them, when performing step 103, specifically, it can be as follows:

[0066] Intercept the single-frequency signal and calculate the phase difference between each element and the reference element .

[0067] Using the relationship between the time delay difference of the signal to each element and the phase difference, calculate the position of the element and the initial phase of each element .

[0068] Calculate the amplitude gain of each element according to the covariance matrix of the signals received by the ultra-short baseline array .

[0069] Specifically, during the data processing in step 103, first, synchronize the received signal with the chirp signal, intercept a section of the calibrated single-frequency signal, and the signal received by the element is as Figure 3 shown, where the red mark is the calibrated single-frequency signal.

[0070] Then, establish the relationship between the time delay difference and the phase difference of the signal received by the element as follows:

[0071] .

[0072] Among them is the frequency of the calibrated single-frequency signal, is the time delay difference between the element and the reference element, is the initial phase, is the phase difference, takes values of , takes values of .

[0073] The time delay difference can be expressed by the following formula:

[0074] .

[0075] where is the speed of sound, is the angle of rotation of the lifting and rotating rod, is the pitch angle. The array and the auxiliary sound source are placed at the same depth. Therefore, . The phase of the signal is obtained by Fourier transform. The Fourier transform is as follows:

[0076] .

[0077] .

[0078] where t is the time, is the time shift,

[0079] The phase difference is obtained by subtracting the phase of each received signal from the phase of the reference signal .

[0080] The above relationships are sorted out to obtain the following formula:

[0081] .

[0082] The matrix expression of this formula can be written as:

[0083] .

[0084] where is the wavelength of the calibrated single-frequency signal, and the relationship with the frequency and the speed of sound is .

[0085] Finally, the least squares method is used to calculate the array element positions and the initial phase , and the calculation process is shown as follows:

[0086] .

[0087] where the matrix , the matrix , the matrix , and H is the conjugate transpose.

[0088] Using the covariance matrix of the received signals, the amplitude gain of each array element is calculated, and the calculation formula is shown as follows:

[0089] .

[0090] where is the element on the diagonal of the covariance matrix.

[0091] In addition, in this application, a conventional beamforming algorithm is also used for DOA estimation. The DOA estimation results before and after array calibration are compared, and the comparison results of 6 groups of data are shown in Table 1. Before array calibration, the average deviation of DOA estimation is 2.26°, and after array calibration, the average deviation of DOA estimation is 0.28°. From the perspective of the average error, the calibration algorithm has significant performance in estimating the target azimuth angle.

[0092] Table 1 Comparison diagram of azimuth angle estimation before and after array calibration

[0093]

[0094] Example Two

[0095] As Figure 6 described, this embodiment provides a calibration system for the position error and amplitude-phase error of an ultra-short baseline array, including:

[0096] A base array coordinate system construction module 601, which is used to sequentially number the M array elements of the ultra-short baseline array, establish a base array coordinate system with the first array element as the reference array element, and determine the coordinate positions of each array element.

[0097] A data acquisition module 602, which is used to fix the ultra-short baseline array at one end of a lifting and rotating rod, fix the auxiliary sound source at the other end, control the rotation angle of the ultra-short baseline array, and collect multiple groups of data.

[0098] An error estimation module 603, which is used to respectively estimate the array element position error and the amplitude-phase error between each channel by using the phase difference and covariance matrix between the signals received by each array element.

[0099] To sum up, this application has the following technical effects:

[0100] 1) In this application, since the time delay of receiving a single-frequency signal between each array element can be replaced by a phase delay, the array element position error and the initial phase error are estimated simultaneously, and the amplitude error of each channel is estimated by using the covariance matrix of the received signal, and the error estimation result is accurate.

[0101] 2) In this application, the rotation of the array is controlled by a lifting and rotating rod, which avoids the movement of the auxiliary sound source, reduces the complexity of the experiment process, and improves the performance of the calibration method.

[0102] 3) The method provided in this application is applicable to the calibration of arrays with various geometric structures, such as uniform linear arrays and circular arrays.

[0103] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification.

[0104] In this article, specific examples are used to elaborate on the principles and implementation modes of this application. The description of the above embodiments is only used to help understand the method and its core idea of this application. At the same time, for those of ordinary skill in the art, according to the idea of this application, there will be changes in the specific implementation modes and application scopes. To sum up, the content of this specification should not be construed as a limitation to this application.

Claims

1. A calibration method for position error and amplitude-phase error of an ultra-short baseline array, characterized in that Including the following steps: Successively number the M array elements of the ultra-short baseline array, establish a base array coordinate system with the first array element as the reference array element, and determine the coordinate positions of each array element; Fix the ultra-short baseline array at one end of the lifting and rotating rod, fix the auxiliary sound source at the other end, control the rotation angle of the ultra-short baseline array and collect multiple groups of data; Utilize the phase differences and covariance matrices between the signals received by each array element to respectively estimate the array element position error and the amplitude-phase errors between each channel; Among them, utilizing the phase differences and covariance matrices between the signals received by each array element to respectively estimate the array element position error and the amplitude-phase errors between each channel specifically includes: Intercept a single-frequency signal and calculate the phase difference between each array element and the reference array element ; Using the relationship between the time delay difference of the signal to each array element and the phase difference, the least squares method is used to calculate the positions of the array elements and the initial phases of each array element ; Calculate the amplitude gain of each array element according to the covariance matrix of the received signals by the ultra-short baseline array ; The relationship between the time delay difference and the phase difference at each array element is specifically: ； Among them, is to calibrate the frequency of the single-frequency signal, is the time delay difference between the array element and the reference array element, is the initial phase, is the phase difference, The value of is The value of ; The calculation formula for the time delay difference is: ； Wherein, is the speed of sound, is the angle of rotation of the lifting and rotating rod, is the pitch angle; Calculate the positions of the array elements using the least squares method and the initial phases of each array element , specifically including: According to the formula , calculate the positions of the array elements and the initial phases of each array element ; Among them, the matrix , the matrix , the matrix , is the wavelength for calibrating the single-frequency signal.

2. A calibration method for position error and amplitude-phase error of an ultra-short baseline array according to claim 1, characterized in that Establishing a base array coordinate system with the first array element as the reference array element specifically includes: Taking the first array element as the origin of the coordinate system, setting its amplitude gain as the reference value and the initial phase as the reference phase, a base array coordinate system is established, and the position coordinates of each array element in the base array coordinate system are .

3. A calibration method for position error and amplitude-phase error of an ultra-short baseline array according to claim 1, characterized in that Fixing the ultra-short baseline array at one end of the lifting and rotating rod, fixing the auxiliary sound source at the other end, controlling the rotation angle of the ultra-short baseline array and collecting multiple groups of data specifically includes: Deploy the ultra-short baseline array and the auxiliary sound source at the same depth in the anechoic water tank; Rotate the ultra-short baseline array through the lifting and rotating rod so that the ultra-short baseline array receives the combined signals emitted by the auxiliary sound source at each rotation angle.

4. A method for calibrating the position error and amplitude-phase error of an ultra-short baseline array according to claim 3, characterized in that The combined signals emitted by the auxiliary sound source are composed of a chirp signal and a calibration single-frequency signal with a fixed frequency.

5. A method for calibrating the position error and amplitude-phase error of an ultra-short baseline array according to claim 1, characterized in that, Calculate the amplitude gain of each array element according to the covariance matrix of the received signals by the ultra-short baseline array , specifically including: According to the formula , calculate the amplitude gain of each array element ; wherein are the elements on the diagonal of the covariance matrix.

6. A calibration system for position error and amplitude-phase error of an ultra-short baseline array, characterized in that, Including: A base array coordinate system construction module, used to successively number the M array elements of the ultra-short baseline array, establish a base array coordinate system with the first array element as the reference array element, and determine the coordinate positions of each array element; A data acquisition module, used to fix the ultra-short baseline array at one end of the lifting and rotating rod, fix the auxiliary sound source at the other end, control the rotation angle of the ultra-short baseline array and collect multiple groups of data; An error estimation module, used to utilize the phase differences and covariance matrices between the signals received by each array element to respectively estimate the array element position error and the amplitude-phase errors between each channel; Among them, utilizing the phase differences and covariance matrices between the signals received by each array element to respectively estimate the array element position error and the amplitude-phase errors between each channel specifically includes: Intercept the single-frequency signal and calculate the phase difference between each array element and the reference array element ; Using the relationship between the time delay difference and the phase difference of the signals arriving at each array element, the least squares method is used to calculate the positions of the array elements and the initial phases of each array element ; Calculate the amplitude gain of each array element based on the covariance matrix of the received signals by the ultra-short baseline array ; The relationship between the time delay difference and the phase difference at each array element is specifically: ； Among them, is to calibrate the frequency of the single-frequency signal, is the time delay difference between the array element and the reference array element, is the initial phase, is the phase difference, The value of is The value of ; The calculation formula for the time delay difference is: ； Among them, is the speed of sound, is the angle of rotation of the lifting and rotating rod, is the pitch angle; Calculate the positions of the array elements using the least squares method and the initial phases of each array element , specifically including: According to the formula , calculate the positions of the array elements and the initial phases of each array element ; Among them, matrix , matrix , matrix , is to calibrate the wavelength of the single-frequency signal.

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